It is the voice that is so familiar. The hair, once red, is now white. The frame, once six foot four, is less imposing now. But the sonorous tones are unmistakable.

There is not even the merest hint of the debilitating stutter with which Jonathan Miller suffered as a boy and adolescent. Although sometimes it can still show itself, particularly when making declarations on subjects he finds objectionable — old sores such as theatre critics, or new ones such as David Cameron’s refusal to follow all of the Leveson Report’s recommendations.

There cannot be many people who have been the target of Miller’s withering ire and not been aware of it. Yet despite recent depictions in the press — “The King of Curmudgeon” one recent article called him — Miller remains the most civilised and civilising man you could hope to meet.

“The choreography is based on Busby Berkeley, you know,” the voice is saying. We are standing in the foyer of the Coliseum in London and the lady to whom Jonathan Miller is talking is clearly a fan. She has just watched the dress rehearsal of the director’s acclaimed English National Opera production of The Mikado. No doubt she will be back next month for the return of Miller’s equally uproarious The Barber of Seville, and then back again in June for his La Bohème.

The ENO has done pretty well out of Miller. He is responsible for directing their longest-running opera productions. His Mikado was first seen 27 years ago, his Barber of Seville is almost as old and is just as fresh and universally praised. Miller gets top billing in the ENO posters, even above the operas’ composers, Gilbert and Sullivan and Rossini.

The Mikado’s return coincides with the publication of the first full-length biography of Miller. Kate Bassett’s fascinating book draws together the many strands that combine to make this renaissance man. And when you consider the variety and number of disciplines that he bestrides — writing, directing, opera, drama, medicine, anthropology, comedy, film and documentary, all of which he has practised to the highest standard — it is hard to think of another polymath as accomplished as this one.

Among its many themes, Bassett’s book explores whether there is a price for having such diverse talents. Miller was drawn to the glamour of the West End and Broadway after the stunning success of the groundbreaking satirical revue Beyond the Fringe, in the 1960s, in which he starred with Peter Cook, Alan Bennett and Dudley Moore.

He went on to direct the still-mesmerising film of Alice and Wonderland, his theatre productions have included Sir Laurence Olivier’s Shylock in The Merchant of Venice, and he has made mind-expanding television documentaries about the human body and atheism. There have been contributions to medical and anthropological research too, but Bassett wonders whether, at the age of 78, Miller has cause to feel regret or even guilt for not spending more time working on the serious business of science, and less on the relatively trivial business of showbiz.

Then there is the question of his Jewishness. On that you have to feel a tad sorry for the man. For someone who has so vociferously rejected the notion of identifying with any group that is narrower than the human race, he has spent an awful lot of time talking about the limits and extent of his Jewishness.

Bassett’s book, called In Two Minds, reveals that the story of Miller’s family is in every significant way, quintessentially Jewish. His father Emanuel was a Cambridge academic and the founder of child psychology; his grandfather Adam was a Lithuanian Jew who settled in the East End and built a business from scratch into one that supplied bearskin hats for the British army. The family of his mother Betty, a novelist, were also immigrants from Lithuania.

But still, it comes as a bit of a surprise that Miller and I have barely said hello before he sounds off on a subject that it had seemed a good idea to broach tentatively.

“The Holocaust has never made me feel Jewish”, he volunteers, before we have even sat down. “We”, by which he means humans, “have killed 250 million of each other between 1900 and 2000. Mao killed nearly 40 million. Stalin killed 20 to 30 million, and then there is the Congo and all of that. The Holocaust is obviously an outrage. But it doesn’t make me feel Jewish.”

There is irony here. Miller’s father, who at Cambridge had joined the atheistic Heretics Society, certainly did feel more Jewish because of the Holocaust. He compelled his son to go to synagogue. The adolescent Jonathan fought tooth and nail against religion, even to the point of laying booby traps for the rabbi who was commissioned by Emanuel to tutor his son. Jonathan won the battle. The result was a permanent schism between father and son.

“I was never very close to him,” says Miller, who manages to speak about his father with admiration and no discernible affection.

Both men have much in common. When Jonathan describes Emanuel, he could almost be talking about himself. “He was a sculptor, a writer, he was the founder of child psychiatry. He wrote several books. He did very good painting and very good sculptures and he was acquainted with a very large amount of literature and art. And yet he would have been astounded if anyone had thought of him as being unusually versatile,” he says, as if to shrug off the admiring descriptions of himself as a polymath.

Miller senior died soon after the success of Jonathan’s 1974 National Theatre production of The Merchant of Venice, with Laurence Olivier’s Shylock. Olivier, who ran the National at the time, approached Miller with a set of what Olivier saw as Jewish props.

Miller recalls: “I wanted to get rid of all the Jewish cliches he came to me with — the noses, teeth, things like that. I said: ‘Just take them off’. I want him to be a businessman who happens to be Jewish and has suffered from antisemitism.”

It is clear that what motivated Miller to rid Olivier of the crude characterisation (the teeth were apparently modelled on those belonging to a Jewish member of the National’s board) was not Miller’s Jewishness, but his abhorrence of anthropological inaccuracy.

“I couldn’t bear getting the cultural details wrong,” he says. “And by that I mean getting wrong the clothes people would be wearing in that particular occupation, at that particular time in the 1890s which is when I set it.”

Did Miller’s father see the production?

“I think he might have seen it? I can’t remember what he thought. I think he felt I wasn’t quite Jewish enough. When I named my two sons Tom and William, my father said to my sister: ‘I see your brother is still striking Anglo Saxon attitudes’, because I wouldn’t give them Jewish names, like…” — and his tone takes on a hint of derision — “Jonathan”.

Engaging Miller in conversation about culture can be fraught with pitfalls. The word is only meaningful to him in an anthropological sense. “Culture is what people do over and above just surviving,” he says breezily, by which he means the clothes people wear, the food they eat, the choices a society makes.

Even so, in a broader sense, Miller has contributed to this country’s cultural life more than most. Perhaps as much as anyone. The seriousness with which he talks about complex subjects, nearly always in grammatically correct, elegant sentences, makes it easy to forget that among the man’s many talents is the ability to impersonate chickens, a skill honed at his old school, St Paul’s. As the title of Bassett’s book suggests, neither the serious nor the showbiz side ever dominates Miller for very long.

As a schoolboy he was larking outside the theatre where Danny Kaye was performing. The American star’s manager was so impressed with Miller’s impersonation of Kaye that he took him to Kaye’s dressing room. Miller reprised his performance which impressed Kaye so much. Kaye asked Miller what he wanted to do when he grew up.

“A doctor,” replied Miller.”

“You will never do it,” said Kaye.

Next month Miller begins rehearsing a production of Gita Sowerby’s 1912 drama Rutherford and Son for Yorkshire theatre company Northern Broadsides.

“It’ll be the last thing I do,” he says dramatically. “I don’t get asked to do much anymore.” And looking up at the ENO’s florid plasterwork, he says “I have no invitation to do anything further here at all.”

That impulse to say out loud the kind of thing most people in his position would only inwardly think remains undiminished. Perhaps it has increased with age.

He continues: “I think it’s mad because as long as you keep your wits about you, it doesn’t matter how old you are. You get better and better as you get older because you’ve seen everything and you become an expert. But the management here don’t seem to recognise that.”

He threads his arms through the sleeves of his puffa coat and then, before stepping out into the cold of St Martin’s Lane, he adds: “Although, they are perfectly happy to profit from my long runs.”